$N_pN_n$ scheme and the valence proton-neutron interaction

TL;DR

This paper investigates the $N_pN_n$ scheme's relation to valence proton-neutron interactions, revealing that the scheme's appearance is mainly due to the general trend of decreasing excitation energy with increasing valence nucleons.

Contribution

It challenges the common belief by showing that the $N_pN_n$ scheme's manifestation is a consequence of a simple trend rather than a direct result of valence proton-neutron interactions.

Findings

The $N_pN_n$-plot simplification is due to decreasing excitation energy with more valence nucleons.

The $N_pN_n$ scheme does not directly reflect the valence proton-neutron interaction.

The observed pattern arises from a general trend, not a specific interaction effect.

Abstract

We examine the common belief that the $N_pN_n$ scheme is manifested as a direct consequence of the valence proton-neutron interaction which has proven to be a dominant factor in developing collectivity in nuclei. We show that the simplification of the $N_pN_n$-plot of the lowest $2^+$ excitation energy is introduced merely because the excitation energy always decreases when the valence nucleon number becomes larger.